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GMAT Diagnostic Test Question 45

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GMAT Diagnostic Test Question 45 [#permalink] New post 29 Sep 2013, 21:08
Expert's post
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

59% (01:36) correct 41% (00:39) wrong based on 204 sessions

GMAT Diagnostic Test Question 45

Field: Algebra
Difficulty: 600


If x=(\sqrt{5}-\sqrt{7})^2, then the best approximation of x is:

A. 0
B. 1
C. 2
D. 3
E. 4
[Reveal] Spoiler: OA

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Last edited by Bunuel on 06 Oct 2013, 23:39, edited 1 time in total.
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Expert Post
Founder
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User avatar
Affiliations: UA-1K, SPG-G, HH-D
Joined: 04 Dec 2002
Posts: 12062
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
WE: Information Technology (Hospitality and Tourism)
Followers: 2219

Kudos [?]: 8157 [0], given: 3640

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Re: GMAT Diagnostic Test Question 45 [#permalink] New post 29 Sep 2013, 21:10
Expert's post
Explanation:
Official Answer: A

x=(\sqrt{5}-\sqrt{7})^2=5-2\sqrt{35}+7=12-2\sqrt{35}.

Since \sqrt{35}\approx{6}, then 12-2\sqrt{35}\approx{12-2*6}=0.

Answer: A.
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Re: GMAT Diagnostic Test Question 45 [#permalink] New post 21 Oct 2013, 09:56
bb wrote:

GMAT Diagnostic Test Question 45

Field: Algebra
Difficulty: 600


If x=(\sqrt{5}-\sqrt{7})^2, then the best approximation of x is:

A. 0
B. 1
C. 2
D. 3
E. 4


We have: 0 < \sqrt{7} - \sqrt{5} = \frac{2}{\sqrt{7} + \sqrt{5}} < \frac{2}{4} = \frac{1}{2}. Therefore, 0< (\sqrt{7} - \sqrt{5})^2 < \frac{1}{4}
The answer is A
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Re: GMAT Diagnostic Test Question 45 [#permalink] New post 23 Feb 2014, 14:29
I'm not sure to understand the logic behind bb's analysis.
My approach was: SQRT(5) is close to 2.2 and SQRT(7) is close to 2.5.
The subtraction should be a decimal number, that becomes even smaller once raised to the 2nd power.
Therefore, the best estimate should be closer to 0 than to 1.
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Re: GMAT Diagnostic Test Question 45 [#permalink] New post 23 Feb 2014, 14:35
Expert's post
Enael wrote:
I'm not sure to understand the logic behind bb's analysis.
My approach was: SQRT(5) is close to 2.2 and SQRT(7) is close to 2.5.
The subtraction should be a decimal number, that becomes even smaller once raised to the 2nd power.
Therefore, the best estimate should be closer to 0 than to 1.


The OA is A, which is 0. The OE uses the square of the difference formula: (a-b)^2=a^2-2ab+b^2.
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Re: GMAT Diagnostic Test Question 45   [#permalink] 23 Feb 2014, 14:35
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